The Rolled Throughput Yield (Yrt) is a Lean Six Sigma metric that provides the expected quality level after multiple steps in a process. If we calculate the Throughput Yield for n process steps as Yt1, Yt2, Yt3,...,Ytn, then:
Yrt = Yt1 * Yt2 * Yt3 * ... * Ytn
For example, suppose there are six possible Critical to Quality steps required to process a customer order, with the Throughput Yields of 99.7%, 99.5%, 95%, 89%, 92.3%, 94%. The Rolled Throughput Yield is calculated as:
Yrt = .997 * .995 * .95 * .89 * .923 * .94 = .728
Thus, only 73% of the orders will be processed defect free. It is interesting to see how bad the Throughput Yield will be, even though none of the CTQ steps are that bad. It all adds up! You can see that as processes become more complex (i.e. more CTQ steps), the defect rates can climb rather quickly.
Learn more about the Lean Six Sigma principles and tools for process excellence in Six Sigma Demystified (2011, McGraw-Hill) by Paul Keller, in his online Lean Six Sigma DMAIC short course ($249), or his online Green Belt certification course ($499).